The limit theorems for random walk with state space ℝ in a space-time random environment |
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Authors: | Wei Gang Wang Zhen Long Gao Di He Hu |
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Institution: | (1) School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, 310018, P. R. China;(2) School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P. R. China;(3) School of Mathematics, Anyang Normal University, Anyang, 455000, P. R. China |
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Abstract: | We consider a discrete time random walk on real number space in a space-time random environment. We state that when the random
environment is i.i.d., under the marginal annealed law, the law of large numbers, iterated law and CLT of the process are
correct. Using a martingale approach, we also state an a.s. invariance principle for random walks in general random environment
whose hypothesis requires a subdiffusive bound on the variance of the quenched mean, under an ergodic invariant measure for
the environment chain.
Research supported by the National Natural Science Fundation of China (10371092) and the Foundation of Wuhan University |
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Keywords: | space-time random environment the law of large numbers CLT iterated law invariance principle |
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